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Nordhaus–Gaddum bounds for total Roman domination
Journal of Combinatorial Optimization, 2017In this paper, the authors discuss Nordhaus-Gaddum bounds for the total Roman domination number. In the introductory part, the authors recollect graph preliminaries, open neighborhood, closed neighborhood, degree, complement of a graph, diameter and corona graph. Also, they give Roman dominating function, total Roman dominating function and total Roman
Amjadi, J. +2 more
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Journal of Combinatorial Optimization, 2021
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Abolfazl Poureidi +2 more
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Abolfazl Poureidi +2 more
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On Total Roman Domination in Graphs
International Conference on Theoretical Computer Science and Discrete Mathematics, 2017A Roman dominating function (RDF) on a graph \(G = (V,E)\) is a function \( f:V \rightarrow \lbrace 0,1,2\rbrace \) satisfying the condition that every vertex u for which \(f(u) = 0\) is adjacent to at least one vertex v for which \(f(v)=2\). A total Roman dominating function on a graph \(G = (V,E)\) is a Roman dominating function \(f : V \rightarrow ...
P. Roushini Leely Pushpam, S. Padmapriea
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Total Roman domination in digraphs
Quaestiones Mathematicae, 2019Let D be a finite and simple digraph with vertex set V (D). A Roman dominating function (RDF) on a digraph D is a function f : V (D) → {0, 1, 2} satisfying the condition that every vertex v with f ...
Guoliang Hao, Wei Zhuang, Kangxiu Hu
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Global total Roman domination in graphs
Discrete Mathematics, Algorithms and Applications, 2017A total Roman dominating function (TRDF) on a graph [Formula: see text] is a function [Formula: see text] satisfying the conditions (i) every vertex [Formula: see text] for which [Formula: see text] is adjacent at least one vertex [Formula: see text] for which [Formula: see text] and (ii) the subgraph of [Formula: see text] induced by the set of all ...
Amjadi, J. +2 more
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Quaestiones Mathematicae, 2015
A set S of vertices is a total dominating set of a graph G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set is the total domination number γt(G). A Roman dominating function on a graph G is a function ƒ : V (G) → {0, 1, 2} satisfying the condition that every vertex u with ƒ(u) = 0 is adjacent to at
Chellali, Mustapha +2 more
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A set S of vertices is a total dominating set of a graph G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set is the total domination number γt(G). A Roman dominating function on a graph G is a function ƒ : V (G) → {0, 1, 2} satisfying the condition that every vertex u with ƒ(u) = 0 is adjacent to at
Chellali, Mustapha +2 more
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Total-Roman Domination Property on Interval Graphs
Pure Mathematics, 2023星利 周
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Total double Roman domination numbers in digraphs
Discrete Mathematics, Algorithms and Applications, 2021Let [Formula: see text] be a finite and simple digraph with vertex set [Formula: see text]. A double Roman dominating function (DRDF) on digraph [Formula: see text] is a function [Formula: see text] such that every vertex with label 0 has an in-neighbor with label 3 or two in-neighbors with label 2 and every vertex with label 1 have at least one in ...
Amjadi, J., Pourhosseini, F.
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Algorithmic Aspects of Outer-Independent Total Roman Domination in Graphs
International Journal of Foundations of Computer Science, 2021For a simple, undirected graph [Formula: see text], a function [Formula: see text] which satisfies the following conditions is called an outer-independent total Roman dominating function (OITRDF) of [Formula: see text] with weight [Formula: see text ...
Amit Sharma, P. V. S. Reddy
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